Answered

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The population o f Charlestown was about 32,000 in 2013 , and the exponential growth rate was 1.2% per year. Write an exponential function describing the population ofCharlestown.

Sagot :

The initial population in 2013 is given to be 32,000

The exponential function can be derived as follows

[tex]P=P_0(\frac{100+r}{100})^n[/tex]

where

[tex]\begin{gathered} P_0=\text{initial population} \\ r=\text{rate of growth} \\ n=n\nu\text{mber of years} \end{gathered}[/tex]

In our case

[tex]\begin{gathered} P_0=32,000 \\ r=1.2 \\ n=n \end{gathered}[/tex]

Upon substituting

[tex]P=32000(\frac{100+1.2}{100})^n[/tex]

This is simplified to give

[tex]P=32000(1.012)^n[/tex]

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